Question

The period of a body under SHM is represented by $T=P^a{D}^b{S}^c$,
where P is pressure, D is density and S is surface tension.
The value of a, b and c are:

• A.
• B. -1,-2,3
• C.
• D.

Answer 1

The correct option is A

By substituting the dimension of each quantity,
we get
$T=$
$=\left[M{L}^{-1}{T}^{-2}{]}^a\right[L^{-3}M{]}^b[M{T}^{-2}{]}^c$
Now comparing the dimenstions of quantities in both sides,
we get $a+b+c=0$, $-a-3b=0$
and $-2a-2c=1$
$\therefore x=-\frac{1}{2}$,
$y=\frac{1}{2}$.